Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic ${\mathrm{GL}}_n$

Jiang, Dihua, Nien, Chufeng, and Stevens, Shaun. "Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$." Journal of the European Mathematical Society 017.4 (2015): 991-1007. <http://eudml.org/doc/277611>.

@article{Jiang2015,
abstract = {The Local Converse Problem is to determine how the family of the local gamma factors $\gamma (s,\pi \times \tau ,\psi )$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi $ of $\mathrm \{GL\}_n(F)$, with $F$ a non-archimedean local field, where $\tau $ runs through all irreducible supercuspidal representations of $\mathrm \{GL\}_r(F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r=1,2,\ldots ,\left[\frac\{n\}\{2\}\right]$. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove the Jacquet conjecture. With this approach, the Jacquet conjecture is proved under an assumption which is then verified in several cases, including the case of level zero representations.},
author = {Jiang, Dihua, Nien, Chufeng, Stevens, Shaun},
journal = {Journal of the European Mathematical Society},
keywords = {irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem; irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem},
language = {eng},
number = {4},
pages = {991-1007},
publisher = {European Mathematical Society Publishing House},
title = {Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm \{GL\}_n$},
url = {http://eudml.org/doc/277611},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Jiang, Dihua
AU - Nien, Chufeng
AU - Stevens, Shaun
TI - Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 4
SP - 991
EP - 1007
AB - The Local Converse Problem is to determine how the family of the local gamma factors $\gamma (s,\pi \times \tau ,\psi )$ characterizes the isomorphism class of an irreducible admissible generic representation $\pi $ of $\mathrm {GL}_n(F)$, with $F$ a non-archimedean local field, where $\tau $ runs through all irreducible supercuspidal representations of $\mathrm {GL}_r(F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r=1,2,\ldots ,\left[\frac{n}{2}\right]$. Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture, we formulate a general approach to prove the Jacquet conjecture. With this approach, the Jacquet conjecture is proved under an assumption which is then verified in several cases, including the case of level zero representations.
LA - eng
KW - irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem; irreducible admissible representation; Whittaker model; local gamma factor; local converse theorem
UR - http://eudml.org/doc/277611
ER -